Related papers: General Covariance-Based Conditions for Central Li…

In a paper that appeared in 2010, C. Tone proved a multivariate central limit theorem for some strictly stationary random fields of random vectors satisfying certain mixing conditions. The "normalization" of a given "partial sum" (or "block…

Using Stein's method, we prove an abstract result that yields multivariate central limit theorems with a rate of convergence for time-dependent dynamical systems. As examples we study a model of expanding circle maps and a quasistatic…

The theory of dependency graphs is a powerful toolbox to prove asymptotic normality of sums of random variables. In this article, we introduce a more general notion of weighted dependency graphs and give normality criteria in this context.…

In this paper we extend a central limit theorem of Peligrad for uniformly strong mixing random fields satisfying the Lindeberg condition in the absence of stationarity property. More precisely, we study the asymptotic normality of the…

We adapt arguments concerning entropy-theoretic convergence from the independent case to the case of FKG random variables. FKG systems are chosen since their dependence structure is controlled through covariance alone, though in the sequel…

A central limit theorem is established for a sum of random variables belonging to a sequence of random fields. The fields are assumed to have zero mean conditional on the past history and to satisfy certain conditional $\alpha$-mixing…

We develope the framework of transitional conditional independence. For this we introduce transition probability spaces and transitional random variables. These constructions will generalize, strengthen and unify previous notions of…

We prove a general transfer theorem for multivariate random sequences with independent random indexes in the double array limit setting. We also prove its partial inverse providing necessary and sufficient conditions for the convergence of…

We apply the concept of distance covariance for testing independence of two long-range dependent time series. As test statistic we propose a linear combination of empirical distance cross-covariances. We derive the asymptotic distribution…

We obtain central limit theorems for stationary random fields employing a novel measure of dependence called $\theta$-lex weak dependence. We show that this dependence notion is more general than strong mixing, i.e., it applies to a broader…

We refine the classical Lindeberg-Feller central limit theorem by obtaining asymptotic bounds on the Kolmogorov distance, the Wasserstein distance, and the parametrized Prokhorov distances in terms of a Lindeberg index. We thus obtain more…

Graphical models are widely used in diverse application domains to model the conditional dependencies amongst a collection of random variables. In this paper, we consider settings where the graph structure is covariate-dependent, and…

When testing for the mean vector in a high dimensional setting, it is generally assumed that the observations are independently and identically distributed. However if the data are dependent, the existing test procedures fail to preserve…

The standard method to check for the independence of two real-valued random variables -- demonstrating that the bivariate joint distribution factors into the product of its marginals -- is both necessary and sufficient. Here we present a…

We present an adaptation of Stein's method of normal approximation to the study of both discrete- and continuous-time dynamical systems. We obtain new correlation-decay conditions on dynamical systems for a multivariate central limit…

This paper is concerned with cross-sectional dependence arising because observations are interconnected through an observed network. Following Doukhan and Louhichi (1999), we measure the strength of dependence by covariances of nonlinearly…

Motivated by open problems in applied and computational algebraic topology, we establish multivariate normal approximation theorems for three random vectors which arise organically in the study of random clique complexes. These are: (1) the…

Study of time series data often involves measuring the strength of temporal dependence, on which statistical properties like consistency and central limit theorem are built. Historically, various dependence measures have been proposed. In…

Motivated by statistical inference problems in high-dimensional time series data analysis, we first derive non-asymptotic error bounds for Gaussian approximations of sums of high-dimensional dependent random vectors on hyper-rectangles,…

We establish the central limit theorem for linear processes with dependent innovations including martingales and mixingale type of assumptions as defined in McLeish [Ann. Probab. 5 (1977) 616--621] and motivated by Gordin [Soviet Math.…